Solution :
Given that,
n = 200
x = 68
Point estimate = sample proportion = = x / n = 68/200=0.34
1 - = 1- 0.34 =0.66
At 95% confidence level the z is ,
= 1 - 95% = 1 - 0.95 = 0.05
/ 2 = 0.05 / 2 = 0.025
Z/2 = Z0.025 = 1.96 ( Using z table )
Margin of error = E = Z/2 * ((( * (1 - )) / n)
= 1.96 (((0.34*0.64) /200 )
E = 0.065
A 95% confidence interval for population proportion p is ,
- E < p < + E
0.34 - 0.065 < p < 0.34+0.065
0.275 , 0.405
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